Weird Blender Subsurface glitch
Subdivision surface only works well with quads, and from the looks of it your model isn't constructed in the most clean way. There are a few things you can try short of remodelling the mesh:


Remove doubles
Recalculate Normals
Add a bevel modifier, which might be able to clean up the edges for you so you can apply a subsurface modifier.
Add 2 edge loops around the perimeter of the object so that subdivision works better.